簡約 ((3m))/((3m^2-1))-1/((2(3m+1)))

解

簡約

\frac{( 3 m )}{( 3 m ^{2} - 1 )} - \frac{1}{( 2 ( 3 m + 1 ) )}

\frac{15 m ^{2} + 6 m + 1}{2 ( 3 m + 1 ) ( 3 m ^{2} - 1 )}

解答ステップ

\frac{3 m}{3 m ^{2} - 1} - \frac{1}{2 ( 3 m + 1 )}

以下の最小公倍数:

3 m^{2} - 1, 2 (3 m + 1) : 2 (3 m + 1) (3 m + 1) (3 m - 1)

LCMに基づいて分数を調整する

= \frac{6 m ( 3 m + 1 )}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )} - \frac{( 3 m + 1 ) ( 3 m - 1 )}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )}

分数の規則を適用する:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{6 m ( 3 m + 1 ) - ( 3 m + 1 ) ( 3 m - 1 )}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )}

簡素化

6 m (3 m + 1) - (3 m + 1) (3 m - 1) : 15 m^{2} + 6 m + 1

= \frac{15 m ^{2} + 6 m + 1}{2 ( 3 m + 1 ) ( 3 m + 1 ) ( 3 m - 1 )}

2つの正方形の差

(3 m + 1) (3 m - 1) を適用します : 3 m^{2} - 1

= \frac{15 m ^{2} + 6 m + 1}{2 ( 3 m + 1 ) ( 3 m ^{2} - 1 )}